Undefined log-mean temperature in heat exchanger design

[mastermechanic]

For a course project, I need to design a heat exchanger to cool electronic components in an UAV. The heat exchanger will be cross-flow air to liquid. The cold side (air side) properties are evaluated at an altitude of 7620 m and -34.5 °C. For the hot side ethylene glycol - water solution with a 60:40 ratio will be used.

Known Parameters

Heat Load: 910 W

Cold Side Hot Side

Mass Flow Rate: 0.023 kg/s Mass Flow Rate: 0.1 kg/s
Specific Heat: 1.005 kJ/kg.K Specific Heat: 3.626 kJ/kg.K
Inlet Temp: - 34.5 °C Inlet Temp: -17.5 °C (from Q = m.c.dt)
Outlet Temp: 4.87 °C (from Q = m.c.dt) Outlet Temp: -20 °CThe problem arises when I try to calculate log-mean temperature,

T_lm = [ (T_h_1 - T_c_2) - (T_h_2 - T_c_1) ] / ln[ (T_h_1 - T_c_2) / (T_h_2 - T_c_1)]

But since (T_h_1 - T_c_2) = ( -17.5 - 4.87) = -22.37 °C and (T_h_2 - T_c_1) = (-20 - (-34.5)) = 14.5 °C

The fraction inside the ln function becomes negative. Where is the problem? I am sure about the temperatures of the air side, therefore, the problem is probably due the temperatures of the hot side.

Although, the air outside is - 34.5°C the cabin of the UAV must be warmer. Considering the radiation from electronics and engine we assumed the cabin temperature as - 20°C and calculated inlet temp. from Q= m.c.dt. I need your help at this point.

 

[256bits]

Inlet Temp: - 34.5 °C Inlet Temp: -17.5 °C (from Q = m.c.dt)
Outlet Temp: 4.87 °C (from Q = m.c.dt) Outlet Temp: -20 °C

4.87 C

 

[mastermechanic]

4.87 C

Sorry, I didn't understand what you meant. What's wrong with 4.87?

 

[256bits]

Sorry, I didn't understand what you meant. What's wrong with 4.87?

Outside air temperature = -34.5 C inlet Cold Air
Cabin temperature = -17.5 C Inlet Hot Fluid

Does it not seem odd that the outlet air temperature will heat up to 4.87 C?